Mathematics, Time, Selfhood

hello everyone and welcome back to active inference insights as always I'm your host darus parvey Wayne and today I have the great pleasure of speaking to Mr although very soon it will be Dr Lance D Costa Lance is a PhD student with Greg pavus and KL friston jointly at Imperial College London in UCL and his work lies at the intersection of mathematics cognitive science and machine learning indeed he is at the very Cutting Edge of the technical formulations underlying AC of inference and so I'm personally looking forward to learning from him today and I hope you are too ladies and gentlemen I bring you Lance the Costa Lance thank you so much I I genuinely meant what I don't really like doing the introduction because it feels so you know sort of a bit stagnant and rigid but I genuinely meant what I wrote there which is that I'm really looking forward to learning than for having me and appreciate the introduction yeah um and you will when when is when is one when do you expect to become a doctor when's that total happening so my defense is at the end of February so oh my gosh it's inth yeah wow fingers crossed I'm sure you'll smash it thanks so before we start getting into the maths I this is very exciting for me because you're the first I would say pretty much pure mathematician we've had on we've had computer scientists we've had cognitive scientists but no one really uh delving into the the nether regions of the maths um you know when I was researching what you're interested in I came across um the fact that you're interested in World models and I'm also very interested in World models so I wanted to start there as's like a teaser before we get into the maths and I wanted to ask whether you could explain what you mean by a world model and how you distinguish that from a self model and the reason why I ask that question is kind of twofold one is that I think the word world models might be slightly misleading because it kind of implies that we're modeling the world and in some sense we are but we're definitely not modeling the entire world so it might be called something like an econ Niche model yeah although that's less catchy and then the other reason is I think there's still an open question at least to my eyes in active inference about whether we are modeling the world and ourselves or whether we're just modeling the world and we fit into that in some way right so it would be great to unpick that if possible yeah that that's actually a Cutting Edge question but I really like it great so let me start by world what I mean what I personally mean by World model is that you as an individual you have always some sensory data coming in off active Visual auditive and so forth and you're going to build a model for what's going on outside that causes your data um now the model that you build is a generative model which means that you can generate kind of factual data about what might happen in the future what might happen if I do this and that uh it's a probalistic model because you're always uncertain about what's going on around in the world and it's also a causal model um this means that you're not um you're not exploiting the well you're not exploiting just the correlations in the data that come in but you're actually explaining the causes of the data something like more powerful than than a statistical model uh now I think you're right in calling it an eon Niche model because I mean the data that we have coming in at any point in time is just from around us and so that's ultimately what we want to model uh when we talk about the free energy principle we say that the brain optimizes its model to maximize accuracy and minimize complexity um in that and and that entails uh having a model that's as simple as possible and therefore you don't want a model things are like too far away from you important from you and so this is why having an eon model as a terminology makes more sense sure so when you talked about world model and self…